Systems and methods for providing astigmatism correction

ABSTRACT

A method of selecting a toric lens by taking into consideration the magnitude and orientation of the posterior cornea and/or the location of the incision axis is described. The magnitude and orientation of the posterior cornea can be calculated as a function of the measured pre-operative orientation of the steep meridian of the anterior cornea.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No.61/871,423 filed on Aug. 29, 2014, the entire contents of which areincorporated herein by reference.

BACKGROUND OF THE INVENTION

Field of the Invention

This application is directed at providing correction for astigmatism,including provision of systems and methods that use parameters that werepreviously not systematically accounted for to improve patient outcomes.

Description of the Related Art

Ophthalmic lenses, such as spectacles, contact lenses and intraocularlenses, may be configured to provide both spherical and cylinder power.The cylinder power of a lens is used to correct the rotationalasymmetric aberration of astigmatism of the cornea or eye, sinceastigmatism cannot be corrected by adjusting the spherical power of thelens alone. Lenses that are configured to correct astigmatism arecommonly referred to as toric lenses. As used herein, a toric lens ischaracterized by a base spherical power (which may be positive,negative, or zero) and a cylinder power that is added to the basespherical power of the lens for correcting astigmatism of the eye.

Toric lenses typically have at least one surface that can be describedby an asymmetric toric shape having two different curvature values intwo orthogonal axes, wherein the toric lens is characterized by a “lowpower meridian” with a constant power equal to the base spherical powerand an orthogonal “high power meridian” with a constant power equal tothe base spherical power plus the cylinder power of the lens.Intraocular lenses, which are used to replace or supplement the naturallens of an eye, may also be configured to have a cylinder power forreducing or correcting astigmatism of the cornea or eye.

Several pervasive problems arise in the selection of the proper toriclens configuration. These problems relate to the need to provide thecorrect lens configuration for the eye as it will exist after surgery.First, conventional selection is based on pre-operative anterior cornealkeratometry. That is, the anterior surface of the cornea is measuredbefore surgery to determine the curvature in orthogonal (e.g.,horizontal and vertical) meridians and the toric lens configuration isselected primarily based upon this measurement. These measurements donot conventionally include measurements or estimates of the curvature ofthe posterior surface of the cornea, which can have a significant impacton a patient's overall astigmatism. Failure to account for the posteriorcorneal astigmatism can contribute to improper selection of toric lensconfiguration, which can require further correction.

Another problem arises from surgical steps taken after standard anteriorcorneal keratometry. That is, surgery can induce or exacerbateastigmatism. In practice, an incision is made at one location of the eyeprior to introducing an intraocular lens into the eye. This incisionchanges the properties of the cornea. The changes can include steepeningor flattening of the cornea along a meridian. If the incision flattensan already lower curvature meridian, the astigmatism also can beincreased. Failure to accurately and systematically account for thecontribution of this surgically induced astigmatism can lead tosub-optimal outcomes.

Astigmatism is sometime characterized as “against-the-rule” or“with-the-rule”. FIG. 1 shows two meridians that may be found to havedifferent curvatures in a cornea with astigmatism. The meridian A is avertical meridian of the anterior surface of the cornea and the meridianB is a horizontal meridian of anterior surface of the cornea. If thecurvature of vertical meridian A is steeper than that of horizontalmeridian B, the eye is said to have “with-the-rule” astigmatism, asdepicted in FIG. 1a . If the curvature of horizontal meridian B issteeper than that of vertical meridian A, the eye is said to have“against-the-rule” astigmatism, as depicted in FIG. 1b . While notalways the case, typically the steep meridian of the anterior cornealsurface tends to change from vertical to horizontal with increasing age,while that of the posterior corneal surface tends to retain itsvertically steep alignment. Thus, posterior corneal astigmatismgenerally contributes to against-the-rule astigmatism. See, Douglas D.Koch et. al. “Contribution of posterior corneal astigmatism to totalcorneal astigmatism,” J Cataract Refract Surg 2012; 38:2080-2087.

As discussed above, surgically induced astigmatism (SIA) can affect boththe magnitude and direction of the principal astigmatic meridians of thecornea. Conventional methods include contribution from SIA based on aninput diopter value provided by a physician at an incision location alsoprovided by the physician. However, interactions between incisionlocation and the orientation of the steep meridian in determiningsurgically induced astigmatism (SIA) are not known or conventionallypart of toric IOL selection. Thus, although conventional methods doaccount for SIA, they do so in an un-controlled manner.

In view of the above discussed unknowns, surgeons have adopted a few“rules of thumb” when selecting an appropriate intraocular lens forimplantation in a patient. For example, one rule of thumb is toover-correct against-the-rule astigmatism and to under-correct with-therule astigmatism. Although, the rules of thumb may provide asatisfactory post-operative refractive outcome for some patients, manypatients require additional correction (e.g., eyeglasses) after surgerydue to the conventional inexact techniques. Even for the patients thathave acceptable outcomes, the use of these rules of thumb complicatesIOL selection for the physician. Accordingly, it would be desirable tohave a method that can more precisely predict the post-surgicalrefractive outcome for most patients.

SUMMARY OF THE INVENTION

As discussed above, posterior corneal astigmatism can affect thepost-operative refractive outcome, e.g., the need for spectacles, inpatients undergoing eye surgery for correcting astigmatic defects.Furthermore, the location of the incision axis can also affect thepost-operative refractive outcome. To improve post-operative refractiveoutcome, there exists a need to improve the accuracy of selection of atoric lens configured with easily obtained inputs. In some cases thesealgorithms and methods are configured to predict the magnitude andorientation of the curvature of the posterior cornea and/or thesurgically induced astigmatism.

The embodiments disclosed herein include algorithms and methods tocalculate the magnitude and orientation of posterior corneal astigmatismand the surgically induced astigmatism based on the steep axis of theanterior cornea. The algorithms and methods can be incorporated in acalculator that can provide a toric lens for implantation into apatient's eye. The algorithms and methods discussed herein can beimplemented as instructions which can be executed by a computerprocessor to provide a toric lens for implantation in to a patient'seye.

A preferred embodiment includes a method of determining an optical powerof a toric lens comprising: receiving a measurement related to ananterior corneal portion of an eye of a patient, wherein the measurementobtained by an ophthalmic diagnostic device; receiving informationrelated to a position of an incision to be made in the eye of thepatient for surgical purpose; and calculating an optical power of atoric lens based only on the received measurement and the receivedposition, wherein the method is performed by a processor by executinginstructions stored in a non-transitory computer medium. The receivingmeasurement related to an anterior corneal portion may include receivingorientation of the steep meridian of the anterior corneal portion.Calculating an optical power of a toric lens may include calculating aposterior corneal cylinder value due to posterior corneal astigmatism,the posterior corneal cylinder value determined by a function of a sineof the orientation of the steep meridian of the anterior cornealportion.

Another preferred embodiment includes a method of determining an opticalpower of a toric lens comprising:

-   receiving a measurement related to an anterior corneal portion of an    eye of a patient, the measurement obtained by an ophthalmic    diagnostic device; receiving a measurement related to a posterior    corneal portion of an eye of a patient, the measurement obtained by    an ophthalmic diagnostic device; receiving information related to a    position of an incision to be made in the eye of the patient for    surgical purpose; and calculating an optical power of a toric lens    based on the received measurement and the received position, wherein    the method is performed by a processor by executing instructions    stored in a non-transitory computer medium. The receiving    measurement related to an anterior corneal portion may include    receiving orientation of the steep meridian of the anterior corneal    portion. Calculating an optical power of a toric lens may include    calculating a value for surgically induced astigmatism, the    surgically induced astigmatism value given by a function of a sine    of the orientation of the steep meridian of the anterior corneal    portion and a function of the position of the incision.

In another preferred embodiment, a method of determining an opticalpower of a toric lens to be surgically implanted in an eye of a patientby an incision made in the eye, the incision made along an incisionaxis, comprises: receiving a measurement related to pre-operativeorientation of the steep meridian of the anterior cornea, themeasurement obtained by an ophthalmic diagnostic device; obtaining aposterior corneal cylinder value indicative of the posterior cornealastigmatism; and calculating an optical power of a toric lens to beimplanted in the eye of the patient based on the pre-operative steepmeridian orientation and the posterior corneal cylinder value, whereinthe method is performed by a processor by executing instructions storedin a non-transitory computer medium. Obtaining the posterior cornealcylinder value may include calculating the posterior corneal cylindervalue from the orientation of the steep meridian of the anterior cornea.A further step may involve calculating a value for surgically inducedastigmatism based on the orientation of the steep meridian of theanterior cornea. The surgically induced astigmatism value may bedetermined by a difference between the orientation of the steep meridianof the anterior cornea and an orientation of the incision axis. Afurther step may involve calculating a post-operative orientation of thesteep meridian of the anterior cornea by adding the surgically inducedastigmatism value to the pre-operative orientation of the steep meridianof the anterior cornea.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention may be better understood from thefollowing detailed description when read in conjunction with theaccompanying drawings. Such embodiments, which are for illustrativepurposes only, depict novel and non-obvious aspects of the invention.The drawings include the following figures:

FIG. 1 is a schematic view of a cornea of the eye illustrating meridiansthat may have differing curvature resulting in astigmatism. FIG. 1aillustrates a cornea having with-the-rule astigmatism. FIG. 1billustrates a cornea having against-the-rule astigmatism.

FIG. 2 illustrates an interval plot of the post-operative refractivecylinder power related to residual astigmatism for patients withdifferent pre-operative orientations of the steep meridian of theanterior cornea who were implanted with a non-toric IOL.

FIGS. 3a and 3b are flow charts illustrating different methods ofcalculating post-operative refractive outcome based on pre-operativeanterior corneal curvature measurements.

FIG. 4 is a block diagram that illustrates aspects of a system that canbe used to implement the method described in FIGS. 3a and 3 b.

FIG. 5 is an interval plot that illustrates a comparison betweenmeasured post-operative refractive cylinder power when implanted with anon-toric IOL and the predicted post-operative refractive cylinder powerfor patients with different orientation of the steep meridian of theanterior cornea.

FIG. 6 is an interval plot illustrating the difference between themeasured pre-operative anterior corneal cylinder power, the measuredpost-operative refractive cylinder power and the predictedpost-operative refractive cylinder power for patients with differentorientation of the steep meridian of the anterior cornea.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Each and every feature described herein, and each and every combinationof two or more of such features, is included within the scope of thepresent invention provided that the features included in such acombination are not mutually inconsistent.

Embodiments of the present invention are generally directed to toriclenses or surface shapes, and/or related methods and systems forfabrication and use thereof. Toric lenses according to embodiments ofthe present invention find particularly use in or on the eyes of humanor animal subjects. Embodiments of the present invention are illustratedbelow with particular reference to intraocular lenses; however, othertypes of lenses fall within the scope of the present invention.

Embodiments of the present invention include prescribing, selectingand/or forming ophthalmic lenses and surfaces configured to reduce, orcorrect, astigmatism that are calculated by taking into considerationcontribution of posterior corneal astigmatism. The contribution ofposterior corneal astigmatism is in some embodiments, calculated bymeasuring the magnitude and orientation of anterior corneal astigmatismprior to surgically implanting the ophthalmic lenses and surfaces.Various embodiments also take into consideration, the effect of thelocation of the surgical incision axis on the overall astigmatism.Compared to conventional toric lens calculators, a calculator thatincludes contribution of the posterior corneal astigmatism and/orsurgically induced astigmatism can provide patients with lower residualastigmatism following surgery, thus improving post-surgical refractiveoutcome.

As used herein, the term “optical power” means the ability of a lens oroptic, or portion thereof, to converge or diverge light to provide afocus (real or virtual), and is commonly specified in units ofreciprocal meters (m-1) or Diopters (D). When used in reference to anintraocular lens, the term “optical power” means the optical power ofthe intraocular lens when disposed within a media having a refractiveindex of 1.336 (generally considered to be the refractive index of theaqueous and vitreous humors of the human eye), unless otherwisespecified. See ISO 11979-2, which is herein incorporated by reference inits entirety for all purposes as if fully set forth herein. Except wherenoted otherwise, the optical power of a lens or optic is from areference plane associated with the lens or optic (e.g., a principalplane of an optic). As used herein, a cylinder power refers to the powerrequired to correct for astigmatism resulting from imperfections of thecornea and/or surgically induced astigmatism.

As used herein, the terms “about” or “approximately”, when used inreference to a Diopter value of an optical power, mean within plus orminus 0.25 Diopter of the referenced optical power(s). As used herein,the terms “about” or “approximately”, when used in reference to apercentage (%), mean within plus or minus one percent (±1%). As usedherein, the terms “about” or “approximately”, when used in reference toa linear dimension (e.g., length, width, thickness, distance, etc.) meanwithin plus or minus one percent (1%) of the value of the referencedlinear dimension.

As used herein, the term “post-operative refractive cylinder power” orthe term “post-operative refractive cylinder outcome refers to thepost-operative spherical and/or the cylinder power measured by anoptometrist or an ophthalmic diagnostic device such as an autorefractor.As used herein, the term “pre-operative anterior corneal cylinder”refers to the cylinder power calculated from measurements associatedwith the pre-operative curvature and orientation of the anterior corneathat are obtained by an ophthalmic diagnostic device such as akeratometer or topographer. As used herein, the term “post-operativeanterior corneal cylinder” refers to the cylinder power calculated frompost-operative measurements associated with the curvature andorientation of the anterior cornea that are obtained by an ophthalmicdiagnostic device such as a keratometer or topographer.

Artificial lenses (e.g., contact lenses or artificial intraocularlenses) can correct for certain visual impairments such as an inabilityof the natural lens to focus at near, intermediate or far distances;and/or astigmatism. Intraocular toric lenses have the potential forcorrecting astigmatism while also correcting for other visionimpairments such as cataract, presbyopia, etc. However, in some patientsimplanted intraocular toric lenses may not adequately correctastigmatism and there may be a residual astigmatism that issubstantially equal to or greater than the amount of astigmatism priorto implantation. In some patients, the implanted toric lenses canover-correct the astigmatism, while in some other patients, theimplanted toric lenses can under-correct the astigmatism. This effect isillustrated in FIG. 2 discussed below.

FIG. 2 illustrates an interval plot of the post-operative refractivecylinder power related to residual astigmatism for different groups ofpatients with different pre-operative orientations of the steep meridianof the anterior cornea who were implanted with a particularimplementation of a non-toric IOL. The different groups of patients hadsimilar pre-operative cylinder powers, although they had differentpre-operative orientations of the steep meridian of the anterior cornea.The measured post-operative refractive cylinder power can be resolvedinto a first orthogonal component represented by J₀ and a secondorthogonal component represented by J₄₅.

It is observed from FIG. 2 that (i) patients having against-the-ruleastigmatism, i.e., steep meridian of the anterior cornea oriented alongapproximately 0 degrees-30 degrees and 150 degrees-180 degrees had apost-operative refractive cylinder power of almost 1.0 D; and (ii)patients having with-the-rule astigmatism, i.e., steep meridian of theanterior cornea oriented along approximately 75 degrees-105 degrees hada post-operative refractive cylinder power less than or equal to about0.5 D. Thus, patients having against-the-rule astigmatism hadsignificant residual astigmatism after being implanted with a non-toricIOL while patients having with-the-rule astigmatism had much lowerresidual amounts of astigmatism after being implanted with a non-toricIOL. From the observations of FIG. 2, it can be concluded that theorientation of the steep meridian of the anterior cornea can affect therefractive outcomes in patients. Accordingly, refractive outcomes can beimproved for patients by taking into account at least the orientation ofthe steep meridian of the anterior cornea.

It is desirable that the measured post-operative refractive cylinderpower be as close to 0 as possible for most of the patients. However, instudies conducted on patients implanted with different implementationsof toric lenses using conventional lens selection techniques, it wasobserved that a group of the patients having against-the-ruleastigmatism, i.e., steep meridian of the anterior cornea oriented alongapproximately 0 degrees-30 degrees and approximately 150 degrees-180degrees are under-corrected, i.e. the measured post-operative refractivecylinder is less than or equal to the measured pre-operative anteriorcorneal cylinder but is not 0. For example, a first orthogonal component(J_(0 XCREF)) of the measured post-operative refractive cylinder powerwas about 0.5 D for patients having against-the-rule astigmatism and afirst orthogonal component of the pre-operative anterior cornealcylinder power (J₀) of about +1.0 D. It was observed from the same studythat a group of patients having with-the-rule astigmatism, i.e., steepmeridian of the anterior cornea oriented along approximately 60degrees-120 degrees are over-corrected, i.e. the post-operativerefractive cylinder as measured shows that the post-operative cylinderhas changed by an amount greater than the measured pre-operativeanterior corneal cylinder and is not 0. For example, the firstorthogonal component (J_(0 XCREF)) of the measured post-operativerefractive cylinder power was about +0.5 D for patients havingwith-the-rule astigmatism and a first orthogonal component of thepre-operative anterior corneal cylinder power (J₀) of about −1.0 D.

One possible reason for the under-correction and over-correction forpatients having different orientations of the steep meridian of theanterior cornea is that the contribution of the curvature of posteriorcornea is not taken into consideration. Currently available tonic lenscalculators use (i) magnitude and orientation of the anterior cornealcurvature, obtained by instruments such as a keratometer; (ii) thelocation of the surgical incision provided by a surgeon and (iii) anestimate of surgically induced astigmatism provided by the surgeon toprescribe an intraocular toric lens. However, the toric lens selectiontechniques currently commercially available do not take intoconsideration the curvature of the posterior cornea and/or the effect ofsurgically induced astigmatism on the location of the incision axis. Asdiscussed above, it is now known that the magnitude and orientation ofthe curvature of the posterior cornea can affect the overall astigmatismand if not taken into account can degrade the post-surgical refractiveoutcome.

It is an object of the present disclosure to implement a toric lenscalculator that also takes into consideration the curvature of theposterior cornea and/or the effect of the location of the surgicalincision on the post-operative refractive cylinder. The curvature of theposterior cornea can be measured by sophisticated diagnostic methodssuch as Scheimpflug, Optical coherence tomography (OCT) orvideokeratography. Alternately, the magnitude and orientation of thecurvature of the posterior cornea can be calculated from the magnitudeand orientation of the pre-operative anterior corneal curvature alone orin combination with other variables. Pre-operative anterior cornealcurvature measurements can be obtained by using diagnostic methods suchas keratometry, topography, etc.

FIGS. 3a and 3b are flow charts illustrating different methods ofcalculating post-operative refractive outcome based on pre-operativeanterior corneal curvature measurements. Having the ability to improvethe prediction of the post-operative refractive outcome can beadvantageous in selecting a toric IOL which when implanted can produce adesired post-operative refractive outcome.

FIG. 3a illustrates a flow chart 3000 that depicts a method ofcalculating the post-operative refractive cylinder from the measurementsof the magnitude and orientation of the pre-operative anterior cornealcurvature and the amount of surgically induced astigmatism provided bythe surgeon. The method includes (i) receiving the measurementsassociated with anterior corneal curvature, as illustrated in block3005; (ii) receiving or calculating the amount of surgically inducedastigmatism (SIA) as illustrated in block 3010; (iii) calculating thepost-operative cylindrical power of the anterior cornea, as illustratedin block 3015; (iv) receiving or predicting a posterior corneal cylindervalue associated with the posterior corneal curvature, as illustrated inblock 3020; (v) selecting a value for the toric IOL, as illustrated inblock 3025 to produce a desired post-operative refractive outcome, e.g.,cylinder power of 0 D or close to 0 D e.g., 0.5 D or less, asillustrated in block 3030.

The measurements associated with anterior corneal curvature can includethe pre-operative anterior corneal cylinder power and the orientation ofthe steep meridian of the anterior cornea. In some implementations, theamount of surgically induced astigmatism can be a number between about0.25 D and about 1.0 D that is provided by the surgeon based on the pastexperience and the location of the surgical incision.

The cylinder power as a result of SIA can be resolved into a firstorthogonal component represented by J₀SIA and a second orthogonalcomponent represented by J₄₅SIA. In some implementations, the first andsecond orthogonal components of the cylinder power as a result of SIAcan be calculated from a function of the pre-operative magnitude andorientation of the steep meridian of the anterior cornea. For example, afirst orthogonal component J₀SIA of the surgically induced astigmatismcan be calculated from the equation

${{J_{0}{SIA}} = {k_{1} + {k_{2} \times \left( \left( \left( {\sin\left( {{{abs}(\varphi)}*\frac{\pi}{180}} \right)} \right) \right) \right)} - 1}},$wherein the variable φ refers to the pre-operative orientation of thesteep meridian of the anterior cornea or an angular difference betweenthe pre-operative orientation of the steep meridian of the anteriorcornea and the incision axis and k₁ and k₂ are constants. As used inthis context, the “incision axis” can be an axis through the mid-pointof the incision. In various implementations, φ can have a value between0 degrees and 180 degrees. In a specific implementation k₁ can have avalue of 0.0082 and k₂ can have a value of 0.4239. As another example, asecond orthogonal component J₄₅SIA of the surgically induced astigmatismcan be calculated from the equation

${{J_{45}{SIA}} = {k_{3} \times \left( {0 - \left( \left( {\cos\left( {{{abs}(\varphi)}*\frac{\pi}{180}} \right)} \right) \right)} \right)}},$wherein k₃ is a constant. In a specific implementation k₃ can have avalue of 0.1499. In various implementations, the constants k₁, k₂ and k₃can be determined using mathematical techniques such as recursion. Thetotal surgically induced astigmatism can be calculated as a vector sumof the first orthogonal component J₀SIA and the second orthogonalcomponent J₄₅SIA. Although, in the implementation discussed herein, thefirst orthogonal component J₀SIA and the second orthogonal componentJ₄₅SIA are calculated using sine and cosine functions, in otherimplementations, they can be calculated using polynomial or othermathematical functions.

In some implementations, calculating the magnitude and orientation ofthe post-operative refractive cylinder power of the anterior cornea, asillustrated in block 3015 can include a summation of the pre-operativeanterior corneal cylinder power and the surgically induced astigmatismthat is either provided by the surgeon or calculated as discussed above.In other implementations, the post-operative anterior corneal cylinderpower can be determined from an algebraic or a geometric function of thepre-operative anterior corneal cylinder power and the surgically inducedastigmatism.

In some implementations, the cylinder power associated with theposterior corneal curvature can be obtained from the measurementsassociated with posterior corneal curvature. In some implementations,the posterior corneal cylinder power can be calculated from a functionof the pre-operative orientation of the steep meridian of the anteriorcornea. In some implementations, the posterior corneal cylinder powercan be calculated from a function of the post-operative orientation ofthe steep meridian of the anterior cornea. For example, a firstorthogonal component J₀IntCyl of the posterior corneal cylinder powercan be calculated from the equation

${J_{0}{IntCyl}} = {k_{4} + {k_{5} \times \left( {\left( \left( {\sin\left( {{{abs}(\omega)}*\frac{\pi}{180}} \right)} \right) \right),} \right.}}$wherein the variable φ refers to the post-operative orientation of thesteep meridian of the anterior cornea and k₄ and k₅ are constants. Asdiscussed above, in various implementations, φ can have a value between0 degrees and 180 degrees. In a specific implementation k₄ can have avalue of −0.2628 and k₅ can have a value of 1.00334. As another example,a second orthogonal component J₄₅IntCyl of the posterior cornealcylinder power can be calculated from the equation

${{J_{45}{IntCyl}} = {k_{6} + {k_{7} \times \left( {0 - \left( \left( {\sin\left( {{{abs}\left( {2*\omega} \right)}*\frac{\pi}{180}} \right)} \right) \right)} \right)}}},$wherein k₆ and k₇ are constants. In a specific implementation k₆ canhave a value of −0.0119 and k₇ can have a value of 0.475. In variousimplementations, the constants k₄, k₅, k₆ and k₇ can be determined usingmathematical techniques such as recursion. The total posterior cornealcylinder power can be calculated as a vector sum of the first orthogonalcomponent J₀IntCyl and the second orthogonal component J₄₅IntCyl.Although, in the implementation discussed herein, the first orthogonalcomponent J₀IntCyl and the second orthogonal component J₄₅IntCyl arecalculated using sine and cosine functions, in other implementations,they can be calculated using polynomial or other mathematical functions.In some embodiments, SIA can be ignored for the purpose of calculatingthe posterior corneal cylinder power, in which case, the post-operativeorientation of the steep meridian of the anterior cornea ω is equivalentto the pre-operative orientation of the steep meridian of the anteriorcornea φ.

FIG. 2 illustrates an interval plot of the post-operative refractivecylinder power related to residual astigmatism for patients withdifferent pre-operative orientations of the steep meridian of theanterior cornea who were implanted with a non-toric IOL. As observedfrom FIG. 3a -1, patients having against-the-rule astigmatism (steepmeridian of the cornea oriented at approximately 0 degrees and atapproximately 180 degrees) had greater amount (approximately 1.0 D) ofresidual astigmatism following surgery as compared to patients havingwith-the-rule astigmatism who has less than 0.5D of residualastigmatism. This difference in the post-operative refractive cylinderpower related to residual astigmatism could be attributed to thecurvature of the posterior cornea or surgically induced astigmatism orboth. It is also noted from FIG. 3a -1 that the post-operativerefractive cylinder power has a sinusoidal dependence to the orientationof the pre-operative orientation of the steep meridian of the anteriorcornea. Thus, it can be inferred that the curvature of the posteriorcornea and/or surgically induced astigmatism can also have a sinusoidaldependence to the pre-operative orientation of the steep meridian of theanterior cornea

In various embodiments, the functional relationship between theposterior corneal cylinder power and the pre-operative orientation ofthe steep meridian of the anterior cornea φ or post-operative steepmeridian of the anterior cornea φ can be determined by (i) obtaining thedifference between the measured pre-operative anterior corneal cylinderpower and the post-operative refractive cylinder power of the anteriorcornea for a number of patients in a population that was provided with anon-toric IOL; (ii) plotting the difference versus the pre-operativeorientation of the steep meridian of the anterior cornea; and (iii)finding trigonometric or polynomial functions that best fit thedifference data.

The functional relationship between SIA and the pre-operativeorientation of the steep meridian of the anterior cornea φ or an angulardifference between the pre-operative orientation of the steep meridianof the anterior cornea φ and the incision axis can be similarlydetermined.

A value for the toric IOL can be added to the received or calculatedposterior corneal cylinder value and the calculated post-operativecylindrical power of the anterior cornea to obtain a desiredpost-operative refractive cylinder value. For example, in someimplementations a toric IOL having a value that provides apost-operative refractive cylinder value of 0 D can be selected forimplantation in a patient's eye.

FIG. 3b illustrates a flow chart 3100 that depicts a method ofpredicting the post-operative refractive cylinder power using themeasurements of the pre-operative magnitude and orientation of theanterior corneal curvature and the location of the surgical incision asinputs. In various embodiments, other inputs such related to themeasurement of the eye or the surgical method can be provided inaddition to the pre-operative magnitude and orientation of the anteriorcorneal curvature and the location of the surgical incision. In oneembodiment of the method 3100, the post-operative refractive cylinderpower is predicted only from the input values of the pre-operativeanterior corneal curvature and the location of the surgical incision.This method of calculation differs from the method 3000 in that theposterior corneal cylinder value is solely calculated from theorientation of the steep meridian of the anterior cornea and thelocation of the surgical axis, for example, by using the equationsdescribed above. If surgically induced astigmatism is taken intoconsideration, then it is solely calculated from the orientation of thesteep meridian of the anterior cornea and the location of the surgicalaxis, for example, by using the equations described above. A value forthe surgically induced astigmatism is not requested from the surgeon.The method includes (i) receiving the measurements associated withanterior corneal curvature, as illustrated in block 3005; (ii) receivinga location for the position of the incision axis, as illustrated inblock 3110; (iii) calculating the post-operative refractive cylinderpower, as illustrated in block 3115; and (iv) selecting a toric IOL thatprovides the desired post-operative refractive cylinder power.

The methods 3000 and 3100 can be implemented as a set of instructionswhich are stored in a non-transitory computer medium and executed by acomputer processor. For example, the methods 3000 and 3100 can beimplemented as a calculator that can be accessed over the internet. Asanother example, the methods 3000 and 3100 can be implemented as amobile application which can be downloaded on a mobile device. As yetanother example, the methods 3000 and 3100 can be implemented as asoftware program that is a part of an instrument. An instrument toimplement the methods described herein can comprise a set ofapparatuses, including a set of apparatuses from different manufacturersthat are configured to perform the necessary measurements andcalculations. Any instrument comprising all needed measurements (ocularand corneal measurements) as well as the needed calculations toimplement the methods described herein, including but not limited to themethods 3000 and 3100 can be considered as an inventive embodiment. FIG.4 is a block diagram illustrating an embodiment of a clinical system 300that can be used to implement the methods described herein, includingbut not limited to the methods 3000 and 3100. The system 300 includesone or more apparatuses capable of performing the calculations,assessments and comparisons set forth in determining the magnitude andorientation of the curvature of the anterior and/or posterior cornea.The system 300 can include a diagnostic device 301, a processor 302, anda computer readable memory or medium 304 coupled to the processor 302.The computer readable memory 304 includes therein an array of orderedvalues 308 and sequences of instructions 318 which, when executed by theprocessor 302, cause the processor 302 to compute the surgically inducedastigmatism and posterior corneal cylinder value discussed above.

The array of ordered values 308 can include one or more desiredrefractive outcomes, data obtained from measurements of the patient'seye, data related to one or more types of available IOL, parameters ofrefractive and diffractive features, etc. In some embodiments, thesequence of instructions 318 can include algorithms to performcalculations, customization, simulation, comparison, etc.

The processor 302 may be embodied in a general purpose desktop, laptop,tablet or mobile computer, and/or may comprise hardware and/or softwareassociated with the device 301. In certain embodiments, the system 300may be configured to be electronically coupled to another device, suchas one or more instruments for obtaining measurements of an eye or aplurality of eyes and/or a laser surgical instrument. Alternatively, thesystem 300 may be adapted to be electronically and/or wirelessly coupledto one or more other devices.

FIG. 5 is an interval plot that illustrates a comparison betweenmeasured post-operative refractive cylinder power when implanted with anon-toric IOL and the predicted post-operative refractive cylinder powerfor patients with different orientation of the steep meridian of theanterior cornea. The predicted post-operative refractive cylinder powerwas obtained by ignoring the contribution of SIA in the method 3000 andusing the equations described above to calculate the first orthogonalcomponent of the posterior corneal cylinder power J₀IntCyl and thesecond orthogonal component of the posterior corneal cylinder powerJ₄₅IntCyl. It is observed from FIG. 5 that the predicted post-operativerefractive cylinder power is approximately equal to the measuredpost-operative refractive cylinder power for patients havingagainst-the-rule astigmatism as well as with-the-rule astigmatism. Thus,improved post-operative refractive outcomes can be achieved for patientshaving against-the-rule astigmatism as well as with-the-rule astigmatismby choosing an appropriate toric lens. In other words, both theunder-correction in patients having against-the-rule astigmatism as wellas the over-correction in patients having with-the-rule astigmatism canbe reduced.

FIG. 6 is an interval plot illustrating the difference between themeasured pre-operative anterior corneal cylinder power, the measuredpost-operative refractive cylinder power and the predictedpost-operative refractive cylinder power for patients with differentorientation of the steep meridian of the anterior cornea. The predictedpost-operative refractive cylinder power is calculated using the methods3000 and 3100 discussed above. In order to obtain the data for the plotsof FIG. 6, a toric IOL was selected based on the predictedpost-operative refractive cylinder power such that the post-operativerefractive cylinder power was as close to 0 as possible. It is observedfrom FIG. 6 that when pre-operative anterior corneal cylinder power haspositive value (e.g., against-the-rule astigmatism shown at bin ‘0’),the measured post-operative refractive cylinder power is slightlypositive, which implies some negligible under-correction. Whenpre-operative anterior corneal cylinder power has positive value, thepredicted post-operative refractive cylinder power without toriccorrection is also positive and is almost equal to the pre-operativeanterior corneal cylinder power. By choosing an appropriate toric lens,the measured post-operative refractive cylinder can be almost 0 and theunder-correction can be reduced.

It is further observed from FIG. 6 that for “with-the-rule” patients(e.g., for bin ‘90’) when pre-operative anterior corneal cylinder powerhas a negative value, the post-operative refractive cylinder power ispositive which implies over-correction. It is further observed from FIG.6 that a reduction in the post-operative cylinder is predicted evenwithout toric correction for patients having with-the-rule astigmatism.That is, the Xpredcref value predicts that without toric correction, thepost-operative refractive cylinder power for these patients will be onaverage about −0.5 diopters. Thus, a lens selection device or method asdiscussed herein can be used to identify a lens that reducesover-correction for these patients. For instance, when pre-operativeanterior corneal cylinder power for these patients has a value of about−1.3 diopters, a toric lens selected by the apparatuses or methodsherein can be one that provides post-operative refractive cylinder powerthat is positive but that has a relatively low magnitude, e.g., withinabout 0.5 diopters of 0. Thus, it can be concluded that by taking themagnitude and curvature of the posterior cornea into consideration,over-correction for patients having with-the-rule astigmatism andunder-correction for patients having against-the-rule astigmatism can bereduced.

The above presents a description of the best mode contemplated ofcarrying out the present invention, and of the manner and process ofmaking and using it, in such full, clear, concise, and exact terms as toenable any person skilled in the art to which it pertains to make anduse this invention. This invention is, however, susceptible tomodifications and alternate constructions from that discussed abovewhich are fully equivalent. Consequently, it is not the intention tolimit this invention to the particular embodiments disclosed. On thecontrary, the intention is to cover modifications and alternateconstructions coming within the spirit and scope of the invention asgenerally expressed by the following claims, which particularly pointout and distinctly claim the subject matter of the invention.

What is claimed is:
 1. A method of determining an optical power of atoric lens, the method comprising: receiving a measurement related to ananterior corneal portion of an eye of a patient, the measurementobtained by an ophthalmic diagnostic device; receiving informationrelated to a position of an incision to be made in the eye of thepatient for surgical purpose; and calculating the optical power of thetoric lens based only on the received measurement and the receivedposition, wherein the method is performed by a processor configured toexecute instructions stored in a non-transitory computer medium which,when executed by the processor, cause the processor to calculate theoptical power of the toric lens.
 2. The method of claim 1, whereinreceiving the measurement related to the anterior corneal portionincludes receiving an orientation of the steep meridian of the anteriorcorneal portion.
 3. The method of claim 2, wherein the calculating theoptical power of the toric lens includes calculating a posterior cornealcylinder value due to posterior corneal astigmatism, the posteriorcorneal cylinder value determined by a function of a sine of theorientation of the steep meridian of the anterior corneal portion.
 4. Amethod of determining an optical power of a toric lens, the methodcomprising: receiving a measurement related to an anterior cornealportion of an eye of a patient, the measurement obtained by anophthalmic diagnostic device; receiving a measurement related to aposterior corneal portion of an eye of a patient, the measurementobtained by an ophthalmic diagnostic device; receiving informationrelated to a position of an incision to be made in the eye of thepatient for surgical purpose; and calculating the optical power of thetoric lens based on the received measurement and the received position,wherein the method is performed by a processor configured to executeinstructions stored in a non-transitory computer medium which, whenexecuted by the processor, cause the processor to calculate the opticalpower of the toric lens.
 5. The method of claim 4, wherein receiving themeasurement related to the anterior corneal portion includes receivingan orientation of the steep meridian of the anterior corneal portion. 6.The method of claim 4, wherein the calculating the optical power of thetoric lens includes calculating a value for surgically inducedastigmatism, the surgically induced astigmatism value given by afunction of a sine of the orientation of the steep meridian of theanterior corneal portion and a function of the position of the incision.